Effective Heisenberg Model Research Articles

Stability of hopfions in bulk magnets with competing exchange interactions

Magnetic hopfions are string-like three-dimensional topological solitons, characterised by the Hopf number. They serve as a fundamental prototype for three-dimensional magnetic quasiparticles and are an inspiration for novel device concepts in the field of spintronics. Based on a micromagnetic model and without considering temperature, the existence of such hopfions has been predicted in certain magnets with competing exchange interactions. However, physical realisation of freely moving hopfions in bulk magnets have so far been elusive. Here, we consider an effective Heisenberg model with competing exchange interactions and study the stability of small toroidal hopfions with Hopf number ${Q}_{\text{H}}=1$ by finding first-order saddle points on the energy surface representing the transition state for the decay of hopfions via the formation of two coupled Bloch points. We combine the geodesic nudged elastic band method and an adapted implementation of the dimer method to resolve the sharp energy profile of the reaction path near the saddle point. Our analysis reveals that the energy barrier can reach substantial height and is largely determined by the size of the hopfion relative to the lattice constant.

Determination of superexchange interactions for the CuO2 chains in LiCu2O2

Starting from ab initio calculations, we derive a five-band Hubbard model to describe the ${\mathrm{CuO}}_{2}$ chains of ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$. This model is further simplified to a low-energy effective Heisenberg model with nearest-neighbor ${J}_{1}$ and next-nearest-neighbor ${J}_{2}$ interactions, combining perturbation theory, exact diagonalization calculations, and density matrix renormalization group results. For realistic parameters we find the corresponding values of these interactions. The obtained effective model is consistent with a spiral-magnetic ground state as experimentally observed. Using symmetry arguments, the spiral state is a sufficient condition for the ferroelectricity observed in the system.

Instability of the magnetic state of MPX3(M=Mn,Ni;X=S,Se) monolayers induced by strain and doping

The instability of magnetic states in two-dimensional magnetic materials plays a crucial role in the application of spintronics. However, the instability mechanism and magnetic state diagram of $M\text{P}{X}_{3}$ ($M=\mathrm{Mn}$ and Ni and $X=\mathrm{S}$ and Se) monolayer with multiple magnetic states remains elusive. In our paper, we investigate the instability of magnetic states using ab initio calculation combined with an effective Heisenberg model. We obtain a series of magnetic state diagrams of $M\text{P}{X}_{3}$ ($M=\mathrm{Mn}$ and Ni and $X=\mathrm{S}$ and Se) monolayer under the approaches of strain and carrier doping. We clarify the instability mechanism that is mainly determined by the nearest-neighbor exchange interaction between magnetic ions, find a higher N\'eel temperature in ${\mathrm{NiPSe}}_{3}$ monolayer, and unveil a considerable increase in hole effective mass along the armchair direction in the ${\mathrm{NiPSe}}_{3}$ monolayer, which leads to giant anisotropy of carrier mobility. Our results provide a useful guidance to design high-performance spintronics devices based on the $M\text{P}{X}_{3}$ monolayer.

First-principles study on the magnetic and electronic properties of the high-pressure orthorhombic phase of MnSe

Exploring the mechanism of unconventional superconductivity has been one of the most important topics in condensed matter physics, while studying the magnetic and electronic properties of the parent compounds of unconventional superconductors can provide helpful clues. Recently, superconductivity in the orthorhombic-phase MnSe was successfully induced by applying high pressure, which makes MnSe the second Mn-based superconductor after MnP. Based on the spin-polarized density functional theory calculations, we have studied the magnetic and electronic properties of the orthorhombic-phase MnSe under high pressure. We show that there may exist strong antiferromagnetic (AFM) fluctuations in a narrow energy window (less than 3 meV/Mn) among an AFM state dubbed AFM3 and a series of staggered $n$-mer AFM states. Here the $n$-mer means that a set of $n$ adjacent spins on a line are parallelly aligned. In the AFM3 state and the $n$-mer AFM states, the Mn spins show AFM coupling along the $x$ axis and ferromagnetic (FM) coupling along the $y$ axis, but respectively host FM and staggered $n$-mer AFM correlations along the $z$ axis. Our calculations indicate that the orthorhombic-phase MnSe exhibits a metallic behavior in the low-energy magnetic states, in good accordance with the previous experimental observations. We also map the calculated energies onto an effective Heisenberg model and obtain the exchange couplings $J$, whose values can serve as a reference for analyzing the data from magnetic measurements. Two usual mechanisms like Fermi surface nesting and electron-phonon coupling can be ruled out as the origin of superconductivity. The magnetic properties in the orthorhombic-phase MnSe under high pressure need future in-depth experimental examination.

Complex magnetic ground states and topological electronic phases of atomic spin chains on superconductors

Understanding the magnetic properties of atomic chains on superconductors is an essential cornerstone on the road towards controlling and constructing topological electronic matter. Yet, even in simple models, the magnetic ground states remain debated. Ferromagnetic (FM), antiferromagnetic (AFM), and spin spiral configurations have been suggested and experimentally detected, while non-coplanar and complex collinear phases have been additionally conjectured. Here, we resolve parts of the controversy by determining the magnetic ground states of chains of magnetic atoms in proximity to a superconductor with Monte-Carlo methods. We confirm the existence of FM, AFM and spin spiral ground states, exclude non-coplanar phases in the model and clarify the parametric region of a $\uparrow\uparrow\downarrow\downarrow$-phase. We further identify a number of novel complex collinear spin configurations, including the periodic spin configurations $\uparrow\uparrow\uparrow\downarrow$, and $\uparrow \uparrow \uparrow \downarrow \uparrow \downarrow \downarrow \downarrow \uparrow \downarrow$, which are in some cases combined with harmonic and anharmonic spirals to form the ground state. We topologically classify the electronic structures, investigate their stability against increasing the superconducting order parameter, and explain the complex collinear order by an effective Heisenberg model with dominant four-spin interactions.

New anti-ferromagnetic tri-transition quaternary perovskites for magnetic cloaking and spintronic applications

Magnetism in new tri-transition A-site ordered quaternary perovskites ACu3V4O12 (A = Mn and Cu) are studied using generalized gradient approximation with Hubbard potential (GGA + U) in the domain of density functional theory. The effective Heisenberg model estimates the magnetic exchange coupling constants (J1, J2 and J3) between the spins of Mn and Cu sites. The exchange constants J1 and J3 in MnCu3V4O12 and Cu(1)Cu3(2)V4O12 reveal their long rang interactions through super exchange mechanism. The ground state magnetic order is explained from the optimized energy curves; which reveal the G-type anti-ferromagnetic (AFM) order of MnCu3V4O12 and A-type AFM order of Cu(1)Cu3(2)V4O12. Heisenberg model and magnetic susceptibility are in well agreement in the estimation of Neel temperature 15.1/50 and 15.6/25 K respectively. There is a strong correlation between the magnetism of the A-site atoms (Mn, Cu(1), and Cu(2)), as well as the metallic character of the B-site atoms (V, as well as the tiny contribution of A-site Cu(2) and Mn atoms). Due to AFM metallic nature it is expected that these compounds could be used in spintronic technology and magnetic cloaking devices.

Light-induced switching of magnetic order in the anisotropic triangular-lattice Hubbard model

The time-dependent exact-diagonalization method is used to study the light-induced phase transition of magnetic orders in the anisotropic triangular-lattice Hubbard model. Calculating the spin correlation function, we confirm that the phase transition from the 120$^{\circ}$ order to the N\'{e}el order can take place due to high-frequency periodic fields. We show that the effective Heisenberg-model Hamiltonian derived from the high-frequency expansion by the Floquet theory describes the present system very well and that the ratio of the exchange interactions expressed in terms of the frequency and amplitude of the external field determines the type of the magnetic orders. Our results demonstrate the controllability of the magnetic orders by tuning the external field.

Quasi-one dimensional magnetic interactions in the three-dimensional hyper-honeycomb framework [(C2H5)3NH]2Cu2(C2O4)3.

The Cu(ii) ions in [(C2H5)3NH]2Cu2(C2O4)3 form a hyperhoneycomb lattice and show no indication of long-range magnetic order down to 60 mK. It has therefore been suggested that [(C2H5)3NH]2Cu2(C2O4)3 is a three dimensional quantum spin liquid. We construct a tight-binding model of [(C2H5)3NH]2Cu2(C2O4)3 from Wannier orbital overlaps. Including interactions within the Jahn-Teller distorted Cu-centered eg Wannier orbitals leads to a highly anisotropic effective Heisenberg model. We show that this anisotropy arrises from interference between different superexchange pathways. This demonstrates that when two (or more) orbitals contribute to the localised spin superexchange can be significantly richer than in the textbook single orbital case. The hyper-honeycomb lattice contains two symmetry distinct sublattices of Cu atoms arranged in coupled chains. We show that one sublattice is strongly dimerized, the other forms isotropic antiferromagnetic chains. Integrating out the strongest (intradimer) exchange interactions leaves extremely weakly coupled Heisenberg chains.

Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe2

We present a theoretical study of single-particle and many-body properties of twisted bilayer WSe$_2$. For single-particle physics, we calculate the band topological phase diagram and electron local density of states (LDOS), which are found to be correlated. By comparing our theoretical LDOS with those measured by scanning tunneling microscopy, we comment on the possible topological nature of the first moir\'e valence band. For many-body physics, we construct a generalized Hubbard model on a triangular lattice based on the calculated single-particle moir\'e bands. We show that a layer potential difference, arising, for example, from an applied electric field, can drastically change the non-interacting moir\'e bands, tune the spin-orbit coupling in the Hubbard model, control the charge excitation gap of the Mott insulator at half filling, and generate an effective Dzyaloshinskii-Moriya interaction in the effective Heisenberg model for the Mott insulator. Our theoretical results agree with transport experiments on the same system in several key aspects, and establish twisted bilayer WSe$_2$ as a highly tunable system for studying and simulating strongly correlated phenomena in the Hubbard model.

Magnetic and Electronic Properties of Complex Oxides from First‐Principles

The theoretical treatment of complex oxide structures requires a combination of efficient methods to calculate structural, electronic, and magnetic properties, due to special challenges such as strong correlations and disorder. In terms of a multicode approach, this study combines various complementary first‐principles methods based on density functional theory to exploit their specific strengths. Pseudopotential methods, known for giving reliable forces and total energies, are used for structural optimization. The optimized structure serves as input for the Green's function and linear muffin‐tin orbital methods. Those methods are powerful for the calculation of magnetic ground states and spectroscopic properties. Within the multicode approach, disorder is investigated by means of the coherent potential approximation within a Green's function method or by construction of special quasirandom structures in the framework of the pseudopotential methods. Magnetic ground states and phase transitions are studied using an effective Heisenberg model treated in terms of a Monte Carlo method, where the magnetic exchange parameters are calculated from first‐principles. The performance of the multicode approach is demonstrated with different examples, including defect formation, strained films, and surface properties.

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB2 Hubbard chains

The ground state (GS) properties of the quasi-one-dimensional AB2 Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, a functional integral representation allows us to derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and total spin per unit cell in the Lieb ferrimagnetic GS of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, including both Zeeman and orbital contributions, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.

Magnon dressing by orbital excitations in ferromagnetic planes of K2CuF4 and LaMnO3

We show that even when spins and orbitals disentangle in the ground state, spin excitations are renormalized by the local tuning of eg orbitals in ferromagnetic planes of K2CuF4 and LaMnO3. As a result, dressed spin excitations (magnons) obtained within the electronic model propagate as quasiparticles and their energy renormalization depends on momentum . Therefore magnons in spin-orbital systems go beyond the paradigm of the effective Heisenberg model with nearest neighbor spin exchange derived from the ground state—spin-orbital entanglement in excited states predicts large magnon softening at the Brillouin zone boundary, and in case of LaMnO3 the magnon energy at the M = (π, π) point may be reduced by ∼45%. In contrast, simultaneously the stiffness constant near the Goldstone mode is almost unaffected. We elucidate physics behind magnon renormalization in spin-orbital systems and explain why long wavelength magnons are unrenormalized while simultaneously energies of short wavelength magnons are reduced by orbital fluctuations. In fact, the -dependence of the magnon energy is modified mainly by dispersion which originates from spin exchange between second neighbors along the cubic axes a and b.

Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems.

We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and spin susceptibility in the magnetic phase are expressed in terms of single-particle quantities. This fact not only can be used for realistic calculations of multiband systems but also allows us to reconsider a general description of many-body effects in the most interesting physical regimes, where the physical properties of the system are dominated by collective (bosonic) fluctuations. In the strongly spin-polarized limit, when the local magnetic moment is well defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.

Magnetic order in four-layered Aurivillus phases

We determine the viability of 4-layered Aurivillius phases to exhibit long-range magnetic order above room temperature. We use Monte Carlo simulations to calculate transition temperatures for an effective Heisenberg model containing a minimal set of required couplings. The magnitude of the corresponding coupling constants has been determined previously from electronic structure calculations for $\mathrm{Bi_5FeTi_3O_{15}}$, for which we obtain a transition temperature far below room temperature. We analyze the role of further neighbor interactions within our Heisenberg model, in particular that of the second-nearest-neighbor coupling within the perovskite-like layers of the Aurivillius structure, as well as that of the weak inter-layer coupling, in order to identify the main bottleneck for achieving higher magnetic transition temperatures. Based on our findings, we show that the most promising strategy to obtain magnetic order at higher temperatures is to increase the concentration of magnetic cations within the perovskite-like layers, and we propose candidate compounds where magnetic order could be achieved above room temperature.

Entanglement teleportation via thermal Wannier edge states in a chiral graphene nanoribbon

We investigate the entanglement teleportation via thermal Wannier edge states in a chiral graphene nanoribbon described by the effective Heisenberg model. The results show that in order to realize quantum teleportation the channel entanglement must be larger than a critical minimum value which depends on the entanglement of the initial input state. We also show that the teleportation fidelity is approximately close to the maximum at lower temperature. In particular, if Coulomb repulsion among electrons is smaller than 1.2 eV, the average fidelity will be larger than 2/3 even at room temperature.

Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models

In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Nevertheless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher-lying bands via the perturbative Schrieffer-Wolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian, if a simple uniform pairing condition on the single-particle states is satisfied, and that the compressibility is diverging as a consequence of an emergent $\text{SU}(2)$ symmetry. This symmetry is broken by second-order interband transitions resulting in a finite compressibility, which we illustrate for a one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the Marzari-Vanderbilt sense are used. Finally, we prove an important inequality $D\ensuremath{\ge}{\mathcal{W}}^{2}$ between the Drude weight $D$ and the winding number $\mathcal{W}$, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.

Interplay of iron and rare-earth magnetic order in rare-earth iron pnictide superconductors under magnetic field**Project supported by the National Natural Science Foundation of China (Grant Nos. 11104274, 11274310, and 11474287) and the Fundamental Research Funds for the Central Universities, China (Grant No. 27R1310020A).

The magnetic properties of iron pnictide superconductors with magnetic rare-earth ions under strong magnetic field are investigated based on the cluster self-consistent field method. Starting from an effective Heisenberg model, we present the evolution of magnetic structures on magnetic field in R/FeAsO (R = Ce, Pr, Nd, Sm, Gd, and Tb) and R/Fe2As2 (R = Eu) compounds. It is found that spin-flop transition occurs in both rare-earth and iron layers under magnetic field, in good agreement with the experimental results. The interplay between rare-earth and iron spins plays a key role in the magnetic-field-driven magnetic phase transition, which suggests that the rare-earth layers can modulate the magnetic behaviors of iron layers. In addition, the factors that affect the critical magnetic field for spin-flop transition are also discussed.

Block Magnetic Excitations in the Orbitally Selective Mott Insulator BaFe_{2}Se_{3}.

Iron pnictides and selenides display a variety of unusual magnetic phases originating from the interplay between electronic, orbital, and lattice degrees of freedom. Using powder inelastic neutron scattering on the two-leg ladder BaFe_{2}Se_{3}, we fully characterize the static and dynamic spin correlations associated with the Fe_{4} block state, an exotic magnetic ground state observed in this low-dimensional magnet and in Rb_{0.89}Fe_{1.58}Se_{2}. All the magnetic excitations of the Fe_{4} block state predicted by an effective Heisenberg model with localized spins are observed below 300 meV and quantitatively reproduced. However, the data only account for 16(3)μ_{B}^{2} per Fe^{2+}, approximatively 2/3 of the total spectral weight expected for localized S=2 moments. Our results highlight how orbital degrees of freedom in iron-based magnets can conspire to stabilize an exotic magnetic state.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half-filling using dynamical mean field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered potential $\Delta$ and the on-site Hubbard U. In both the methods we find that for a finite $\Delta$ and at zero temperature, anti-ferromagnetic (AFM) order sets in beyond a threshold $U=U_{AF}$ via a first order phase transition below which the system is a paramagnetic band insulator. Both the methods show a clear evidence for a transition to a half-metal phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both the methods have good qualitative and quantitative consistency in the intermediate to strong coupling regime. On increasing the temperature, the AFM order is lost via a first order phase transition at a transition temperature $T_{AF}(U, \Delta)$ within both the methods, for weak to intermediate values of U/t. But in the strongly correlated regime, where the effective low energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. As a result, at any finite temperature T, DMFT+CTQMC shows a second phase transition (not seen within DMFT+IPT) on increasing U beyond $U_{AF}$. At $U_N > U_{AF}$, when the Neel temperature $T_N$ for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second order transition. In the 3-dimensonal parameter space of $(U/t,T/t,\Delta/t)$, there is a line of tricritical points that separates the surfaces of first and second order phase transitions.

Symmetry-breaking 60°-spin order in theA-site-ordered perovskiteLaMn3V4O12

The magnetism of the A-site-ordered perovskite $\mathrm{LaM}{\mathrm{n}}_{3}{\mathrm{V}}_{4}{\mathrm{O}}_{12}$ is studied comprehensively by means of neutron powder diffraction experiments and theoretical calculations. Magnetic neutron diffraction results show that a rhombohedral 60\ifmmode^\circ\else\textdegree\fi{} spin structure emerges on the cubic lattice below a 44-K N\'eel transition. Ab initio electronic structure calculations confirm that high-spin ${\mathrm{Mn}}^{2+}$ moments are localized while V $3d$-band states are itinerant, and that the noncollinear 60\ifmmode^\circ\else\textdegree\fi{} spin structure is more stable than collinear ferromagnetic or G-type antiferromagnetic alternatives. Effective Heisenberg model calculations reveal that the appearance of such a nontrivial spin structure can be attributed to significant next-nearest-neighbor and third-nearest-neighbor magnetic interactions.